2C+Geometric+Sequences

Stefen McCone A geometric sequence is a sequence with the ratio between two consecutive terms. Also called the common ratio.

=Geometric Sequences:=

A geometric sequence is a sequence that has a generator that is either multiplication or division.
 * What is a geometric sequence?**

Its graph is a curve, much resembling half of a parabola.
 * What does its graph look like?**

Initial Term+ Generator (To The Power of the Term That You Are Solving For)= Output
 * What is the equation?**

The terms do not have a constant difference, but their generators have a common multiple.
 * What do the terms look like?**

The staircases are the differences between the terms.
 * What do the staircases mean?**

The initial value is also the y-intercept.
 * What does the initial value mean?**

Marjorie Moreno Geometric sequence is a sequence in which each term after the first term //a// is obtained by multiplying the previous term by a constant //r//, called the common ratio. It is obvious that //a// ≠ 0 and //r// ≠ 0 or 1. 1, 2, 4, 8, 16, 32, . . . is a geometric sequence. Each term of this geometric sequence is multiplied by the common ratio 2.

Geometric series is the indicated sum of the terms of a geometric sequence. For the geometric sequence 1, 2, 4, 8, 16, 32, 1 + 2 + 4 + 8 + 16 + 32 is the corresponding geometric series.

Practice: Find the 5th term and the common ratio 2,6,18 A. 54 B. 3 C.162 D. 164 the 5th term would be 54(3) = 162
 * Choices:**
 * Correct Answer: C**
 * Solution:**
 * Step 1:** the common ratio is 3. 2(3) = 6 6(3) = 18
 * Step 2:** so r = 3 the 4th term would be 18(3) = 54